РР 4 (Интегралы) МТ-120101 (2013)

1.

sin 3 2x dx 2. 1 3x 4 dx 3.

5

x

dx

2

3x

1

2

x

4x2 32x 52

4.

x 3 sin 5xdx

5. x

2 e

dx 6.

dx

x2 6x 5 x 3

1 2x 3

5

dx

7. 0

dx 8.

0 2x 3x 1

x 2 3

4

16 x

2

2

6

dx

9. sin

xdx 10.

x

4

0

2

1

7dx

1

2xdx

11.

12.

2

4x ln 5

1 x

4

x

0

x 7 1 sin t cos t

,

t

:

.

6

6

y 7 1 sin t sin t

16.

,

,

,

Ox :

y x 2 , y

.

x

17.

,

1

4

Ox : y

1

x x

,

x

.

3

3

3

1.

cos 3 2x dx 2. 3

dx

3.

2x 1

2 dx

2 x

5 3x

2x4 7x3 3x 30

2

x

4.

x 7 cos 2xdx 5. x

x 1 e

dx 6.

dx

x2 2x 3 x 2

3

2x2

4

0

1 ex

7.

dx 8.

dx

x

3

x

2

x

x

2

1

ln 31 e

1

2

1 x2 3 dx

9.

cos5 xdx 10.

0

0

xdx

1 3 e3

1 x

11.

4

12.

dx

16x

1

x

2

1

0

x 2t 2 cost

t

3

:

, 0

.

y 2t2 sin t

2

16.

,

,

,

Ox :

y 3 cos x, y cos x,

0 x 0,5 .

17.

,

Ox :

y

8 0,5x2

, 0 x 4 .

1.

sh 3x 2 dx 2. 3

dx

3.

3x 4

dx 4.

x 2 cos 3xdx

5 3x

2

5 2x

x

2

x cos xdx 6.

2x4 8x3 45x 61

5.

dx

x2 5x 6 x 1

x2 3

x2dx

10

3 7

7.

dx 8.

x

3

x

2

6x

9 x

3

8

0

1

dx

2

9.

cos x cos3x cos 5xdx

10.

3

0

x2

1 x2

3

3

arctg2x

2 3

3

ln 2 3x dx

11.

dx 12.

2

0

1 4x

0

2 3x

x 6 1 sin t cos t

t 0 .

:

,

2

y 6 1 sin t sin t

16.

,

,

,

Ox :

y x 2 , y 3

.

x

17.

,

Ox :

2

y

3 x2

, 0 x

.

3

3

7

2x 5

dx

1. sh 3x 7 dx 2. 1 4x

dx 3.

5x

2

1

4. x 4 sin 3xdx

5. xsin

2

xdx 6.

2x4 7x3 7x2 8x

dx

x2

5x 6 x 1

3

x7dx

1

x2dx

7. 2

8.

0

1 x4

1 x 4

1 tgx

2 x

3

1

3

4

2 dx

9.

dx 10.

x

4 x

sin 2x

1

6

dx

sin xdx

11.

12.

x

2

3x 2

7

cos

2

x

3

2

1

x

cos t ln t sin t

t

, 2

t 3.

:

,

Ox :

1.

cos 2 3x dx 2.

3

dx

3.

1 2x

dx

2

3x

2

3

4x

2

2

x

6x2dx

4.

x 1 cos 7xdx

5. x

x e

dx 6.

x2

3x 2 x 1

1

x5dx

4

dx

7.

8.

2x 1

1 x 2

0 1

x

x

2

9.

cos

cos

dx 10. x2 4 x2 dx

0

2

3

0

2

dx

2

e

tgx

11.

x

12.

dx

4

cos

2

0 3

x3 8

0

x

,

Ox :

1. ch 2x 5 dx 2.

2dx

3.

x 1

dx

2

5

2x

2

3

4 3x

2

x

12dx

4. x 7 cos 2xdx 5. x

1 e

dx 6.

x2

2x 3 x 2

2x2

4

x2dx

3

3 7

7.

dx 8.

x

3

x

2

9 x

3

2

x 1

0

x

1 2

4

dx

9.

sin 4

dx 10.

x

3

0

2

0

1 x2

x3dx

5

x2dx

11.

16x

4

1

12.

31 x

3

1

0

1

x t 2 sin t 2t cos t

t 3 .

:

, 0

y t 2 cost 2t sin t

16.

,

,

,

Ox :

y sin x, y 2 sin x,

0 x .

17.

,

Ox : y x3 , 0 x 2 .

1.

sin 5x 3 dx 2. 3

dx

3.

x 1

dx

9x 1

2

7x

4

x 3 sin 5xdx 5.

xdx

2x4

8x3 17x 5

4.

6.

dx

cos2 x

x2

2x 3 x 2

1

xdx

ln 5

x

x

2

7.

8. e

x e

1dx

3

e

1

x 1

0

3

3

4

x

2

4 dx

2

9.

sin6 xdx 10.

0

2

x

xdx

2

etgx

11.

12.

dx

16x

4

1

cos

2

0

0

x

x sin 2t

, 0 t

3

.

:

y 2sin 2 t

2

16.

,

,

,

Ox :

y x , y , x 0 .

17.

,

28

1-6 .

1.

sin 7x 1 dx 2.

dx

3

3.

2x 1

2 dx

1 x

5 3x

x 6 sin

x

x

2

x

1 e

x

dx 6.

2x4 7x3 7x2 8x

dx

4.

dx 5.

2

x2 5x 6 x 1

3

dx

e3

ln x

dx

7.

8.

2

x 1 ln

2

2

x 1 x 1

e2

x

7 3

3

x3

7 x2 dx

9.

tg4 xdx 10.

0

4

x2dx

1

ln 2dx

11.

12.

x3

4

1

x ln

2

1 x

0 3

8

1 2

x 2t cos t

:

, 0 t 0,75 .

y 2t sin t

16.

,

,

,

Ox :

1.

cos 5x 6 dx 2. 1 4x 5 dx 3.

2x 4

dx

2

x 16

4.

xsin 3xdx

5. xsin

2

xdx 6.

6x4dx

x2 1 x 2

5

dx

ln 2

dx

7.

8.

x

2

x 1

e

x

1 e

2 x

4

0

9.

4

xsin

2

xdx 10.

4

16 x2

dx

cos

x

4

0

2

dx

1

xdx

11.

12.

x

2

3x 2

4

3

0

1 x

3

t

x 6cos

cost

3

3

:

,

t

0 .

t

2

3

y 6 cos

sin t

3

16.

,

,

,

Ox :